Elementary Geometry for College Students (7th Edition)

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 4 - Section 4.1 - Properties of a Parallelogram - Exercises - Page 188: 10


$m \angle A = 63^{\circ}$ $m \angle B = 117^{\circ}$ $m \angle C = 63^{\circ}$ $m \angle D = 117^{\circ}$

Work Step by Step

The opposite angles of a parallelogram have equal measures. We can find the value of $x$: $m \angle A = m \angle C$ $2x+3 = 3x-27$ $x = 30$ We can find the measure of $\angle A$: $m \angle A = 2x+3 = (2)(30)+3 = 63^{\circ}$ We can find the measure of $\angle C$: $m \angle C = 3x-27 = (3)(30)-27 = 63^{\circ}$ Let $a = m\angle B = m \angle D$ The sum of the four angles in a parallelogram is $360^{\circ}$ We can find the value of $a$: $63^{\circ}+a+63^{\circ}+a = 360^{\circ}$ $2a+126^{\circ} = 360^{\circ}$ $2a = 360^{\circ}-126^{\circ}$ $2a = 234^{\circ}$ $a = 117^{\circ}$ Then: $m\angle B = m \angle D = 117^{\circ}$
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